The drawing tension is a critical parameter in the production of optical fibres. Fibre tension has generally been monitored mechanically by measuring the deformation of the fibre in response to a force applied transversely to the direction of movement of the fibre. Specifically, a three wheel strain gauge has been used wherein two wheels are applied to one side of the fibre and third wheel is applied to the other side of the fibre during the start-up of the fibre drawing process. The location of the third wheel relative to the first two wheels is used as a measure of the tension in the fibre. This method has numerous disadvantages. It is difficult to precisely align the device with the fibre so as not to change the original path of the fibre. Contact of the three wheel device with the fibre affects the on-line fibre diameter feedback loop so as to degrade diameter control. Also, the moving fibre can break when contacted by the three wheel device and in this connection this method cannot be used at drawing speeds now obtainable because of fibre breakage problems.
It is therefore desirable to provide a non-contact method of monitoring tension in a fibre being drawn from a preform.
An article entitled `An On-Line Fiber Drawing Tension and Diameter Measurement Device` in the Journal of Lightwave Technology, Vol. 7, No. 2, February 1989 discloses a method of measuring tension which interrogates the fibre transversely during drawing with unpolarized light and then uses the retardation of the scattered light beams to determine draw tension and diameter. Although this method does not contact the fibre, the accuracy is degraded by movement of the fibre within the field of the optics, residual thermal stress, and elipticity of the outer diameter. Because of the sensitivity of the technique to any elipticity, it cannot be used on stress birefringent polarization maintaining fibres, which have large, asymmetric stress regions. Furthermore, twist is often induced in fibres during drawing, and this technique would be especially sensitive to rotation of the ellipse caused by changes in the fibre twist.
Another non-contact method which has been proposed is based on the vibration mode of the drawn fibre which is related to the tension applied to the drawn fibre.
In this connection for a flexible fibre of mass .mu. per unit length stretched under tension F. taking the x-axis as the undeflected position of the fibre and assuming a small lateral deflection y of the fibre which is at right angles to the x axis, the change in tension with deflection is negligible and can be ignored, and the equation of motion for the element in the y-direction is: ##EQU1## where f(x,t) is the magnitude per unit length of any externally applied force.
If the fibre is stretched between two fixed points with distance 1 between them, the boundary conditions are y(0,t)=y(1,t)=0 and f(x,t)=0. The solution will contain many of the normal modes and the equation for the displacement may be written as: ##EQU2##
Each n represents a normal-mode vibration with natural frequency determined from the equation: ##EQU3## C.sub.n and D.sub.n depend on the boundary conditions and the initial conditions.
For a flexible fibre, moving at a constant longitudinal velocity, the natural resonance frequency is given by: ##EQU4## where v is the speed of the longitudinal motion of a fibre.
The effect of speed is negligible in practice and equation (4) provides a satisfactory relationship between natural frequency and tension.
Derivable from equation for n=1 is the relationship between tension, fundamental frequency and fibre diameter:- F=.alpha.+.beta.d.sup.2 f.sup.2 -(4A) where d is the diameter of the drawn fibre and .alpha. and .beta. are experimentally determined constraints.
U.S. Pat. No. 4,692,615 discloses a method based on the vibration mode of the drawn fibre in which the tension in a moving fibre is monitored by sensing vibration motion of the fibre in a direction transverse to the direction in which the fibre is moving. Analysis of the vibration motion by Fast Fourier Transform (FFT) analysis is used to determine at least one frequency component thereof, and the determined frequency component is monitored so as to provide the tension readout in the fibre. However, measuring the frequency response of the fibre to either vibrations within the fibre due to the drawing process or to an intentional perturbation of the fibre position by puffs of air has certain disadvantages. Vibrations in the fibre can be caused by building and apparatus vibrations, preform feed motor instabilities, fibre drawing motor instabilities and/or polymer coating application instabilities, to mention a few. Whilst some of these vibrations, such as building vibrations, would remain constant in frequency and, therefore, are relatively easy to identify, sources such as motor noises would increase in frequency with drawing speed and are much more difficult to isolate from the fundamental fibre vibration. Also, quick puffs of air which are used to cause additional vibration of the fibre can cause fibre diameter feedback loops to become unstable and result in fibre diameter excursions.
U.S. Pat. No. 5,079,433 also discloses a method based on the vibration mode of the drawn fibre in which the motion of the fibre is sensed in a direction transverse to the direction in which the fibre is moving. The sensed movement is analysed by FFT analysis to determine a plurality of frequency components thereof and the fundamental natural frequency of the drawn fibre is identified by a complex procedure which involves identifying the highest peaks of the power spectrum obtained from the FFT analysis and analysing those peaks for the presence of a second harmonic. Using this method, it can be very difficult to extract the basic frequency which relates to tension in the fibre. This is due to the effect of noise, present in the fibre vibration signal, which under certain circumstances, has a second harmonic in the same frequency band.
The use of a FFT analysis to obtain the power spectrum suffers from leakage which is caused by truncation of the time-series record. The leakage problem becomes particularly acute for short data records where the Uncertainty Principle based on the product of resolution bandwidth and signal duration does not allow good frequency resolution. In the fibre drawing process, any external excitation to the drawn fibre is not allowed. FIG. 1 shows the typical fibre vibration signal obtained during the fibre drawing process. FIG. 2 shows the power spectrum of the fibre vibration using FFT analysis. The fibre resonance is difficult to identify in the vibration of the drawn fibre due to the leakage and some noise from external vibrations such as motor instabilities, building and preform vibrations. In some cases, the amplitude of the vibration caused by external sources is bigger than that caused by fibre resonance.
As will be appreciated from FIG. 2, even if it were known that the natural frequency of the drawn fibre fell within a narrow band of, say, 10 Hz it would still be impossible to identify which peak of the spectrum related to the natural frequency.
One object of the present invention is to overcome this problem associated with analysing the sensed motion using a FFT. Broadly, this is achieved by analysing the sensed motion of the drawn fibre transverse to its drawing direction using a time-series model.
It is possible to derive the mathematical model for a dynamic system based on physical laws, and this enables us to calculate the value of some time-varying quantity at any particular instant of time. A model which makes exact calculation possible would be entirely deterministic. However, very few dynamic systems are totally deterministic because changes due to unknown or unquantified effects may take place during the process. It is thus convenient to construct stochastic models that may describe the dynamics of systems. A time-series modelling technique uses discretely sampled data at the input/output of a physical system to develop the stochastic model. In this way, the characteristics of the system can be studied from the behaviour of measured data. Time-series models can also be transformed into the frequency domain in which spectral analysis can be implemented. Using time-series model estimation for the power spectral density gives a smoother curve than that obtained with a FFT without the leakage problem and also a narrower bandwidth for the resonance peaks. For the general multi-input single-output linear model structure: ##EQU5## where yn! is the output signal, un! is the input signal, ak! and bk! are parameters of time-series model, and en! is a white noise.
The input signal un! of the measured system is not usually available for purposes of spectral analysis. For the drawn fibre vibration, its input signal is unmeasured and its output is the motion in the transverse direction, and an autoregressive model is appropriate.
In a p-th order autoregressive (AR) model for time-series y(n), where n is the discrete time index, the current value of the measurement is expressed as a linear combination of p previous values: ##EQU6## where en! designates a white noise. In this case, yn! is the measured position signal of bare fibre in the transverse direction and ak! are the model parameters.
The frequency characteristic analysis can be obtained by the autopower spectral density. The AR power spectral density is given by: ##EQU7## and T is the sampling interval. P.sub..rho. is the white noise variance.
FIG. 3 shows the power spectrum of the fibre vibration obtained using the time-series analysis method. The vibration signal is the same signal as that in FIG. 1. It can be seen that the curve of the spectrum is smoother than that in FIG. 2 and without the leakage problem.